Detecting milli-Hz gravitational waves with optical resonators

TL;DR

The paper argues that the milli-Hz gravitational-wave band, largely untouched by current detectors, can be probed from Earth with a network of ultrastable optical cavities and clock-based references. It introduces a phase-based detection principle where gravitational waves modulate the light’s phase between mirrors, rather than altering cavity length, and shows how two orthogonal cavities plus an optical atomic reference can extract GW signals via multiple beat channels. The authors assess noise sources and propose strategies (cryogenic silicon spacers, long effective optical paths, and active stabilization) to reach meaningful sensitivity, demonstrating potential detections of galactic binaries, MBH mergers, and a stochastic background, along with localization benefits from Earth’s rotation. They further illustrate the science impact with SNR estimates for representative sources and discuss a roadmap toward a global mid-band detector network that complements future space missions and dark-fibre clock networks.

Abstract

We propose a gravitational wave detector based on ultrastable optical cavities enabling the detection of gravitational wave signals in the mostly unexplored $10^{-5}-1$ Hz frequency band. We illustrate the working principle of the detector and discuss that several classes of gravitational wave sources, both of astrophysical and cosmological origin, may be within the detection range of this instrument. Our work suggests that terrestrial gravitational wave detection in the milli-Hz frequency range is potentially within reach with current technology.

Figures (2)

• Figure 1: a) Schematic of the proposed GW detector. The detector consists of two ultrastable lasers at frequencies $f_\text{A}$ and $f_\text{B}$ and one optical atomic reference at frequency $f_{\text{atom}}$. The detection channels $\Delta f_i$ can be realized by beating the laser beams. b) A global network of detectors in the milli-Hz range
• Figure 2: Strain sensitivity $h_{\text{RMS}}=\sqrt{S_y(f)f}$ as a function of the frequency for a detector comprising two orthogonal cavities and an atomic reference, compared to GW signals from several source classes. The light blue shaded area is the parameter space accessible with ultra-low expansion glass cavities, while the patterned area with cryogenic silicon cavities. The continuous lines are the characteristic strains produced by the coalescence of optimally orientated binaries of equal mass, non-spinning black holes. The green dotted line corresponds to the quasi-monochromatic characteristic amplitude produced by a galactic stellar mass binary black hole with chirp mass ${\cal M} = 3.4$ M$_{\odot}$ at a distance of $D=1\,\mathrm{kpc}$ and observed for $T_\mathrm{obs}=3$ years. The magenta dot shows the characteristic amplitude of a double white-dwarf progenitor of a type IA supernova at 1 kpc. The dashed line is the effective characteristic strain produced with signal-to-noise ratio of 1 by a stochastic background with an energy density $\Omega_{GW}= 10^{-6}$ assuming the correlation of the data streams of ten optimally orientated detectors for $T_\mathrm{obs}=3$ years. See SuppMat for details.